I couldn't find anything to support the claim, although that doesn't necessarily mean it's false.
The 1994 Shorter Slang Dictionary (Partridge, Beale, Fergusson) has another meaning:
off-beat unconventional. Adopted from the USA around 1960.
And the 2008 New Partridge Dictionary of Slang and Unconventional English says:
offbeat adjective unconventional, but not unique US, 1938
This has an origin in music.
Beat also has a policing meaning:
In police terminology, a beat is the territory and time that a police officer patrols. Beat policing is based on traditional policing (late 19th century) and utilises the close relationship with the community members within the assigned Beat to strengthen police effectiveness and encourage cooperative efforts to make a safer community. Beat police typically patrol on foot or bicycle which provides more interaction between police and community members (good and bad).
This is just guesswork, but perhaps there's some confusion with a police officer coming "off the beat" to work in the office or to retire.
Another Chennai Slang webpage says this:
Word/phrase: OB adikaradhu
Meaning in context: To waste time.
Origin, usage: OB is pronounced as the individual letters O and B. Etymology not known for certain. Possibly from "Off Beat", old British military term meaning "off duty". Also possibly from "Out of Business" or from "O'l Bhajanai" (local slang for "doing nothing").